# Copyright 2013, Michael H. Goldwasser
#
# Developed for use with the book:
#
#    Data Structures and Algorithms in Python
#    Michael T. Goodrich, Roberto Tamassia, and Michael H. Goldwasser
#    John Wiley & Sons, 2013
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.


class Graph(object):
	"""Representation of a simple graph using an adjacency map."""

	# ------------------------- nested Vertex class -------------------------
	class Vertex(object):
		"""Lightweight vertex structure for a graph."""
		__slots__ = '_element'

		def __init__(self, x):
			"""Do not call constructor directly. Use Graph's insert_vertex(x)."""
			self._element = x

		def element(self):
			"""Return element associated with this vertex."""
			return self._element

		def __hash__(self):  # will allow vertex to be a map/set key
			return hash(id(self))

		def __str__(self):
			return str(self._element)

	# ------------------------- nested Edge class -------------------------
	class Edge(object):
		"""Lightweight edge structure for a graph."""
		__slots__ = '_origin', '_destination', '_element'

		def __init__(self, u, v, x):
			"""Do not call constructor directly. Use Graph's insert_edge(u,v,x)."""
			self._origin = u
			self._destination = v
			self._element = x

		def endpoints(self):
			"""Return (u,v) tuple for vertices u and v."""
			return (self._origin, self._destination)

		def opposite(self, v):
			"""Return the vertex that is opposite v on this edge."""
			if not isinstance(v, Graph.Vertex):
				raise TypeError('v must be a Vertex')
			return self._destination if v is self._origin else self._origin
			raise ValueError('v not incident to edge')

		def element(self):
			"""Return element associated with this edge."""
			return self._element

		def __hash__(self):  # will allow edge to be a map/set key
			return hash((self._origin, self._destination))

		def __str__(self):
			return '({0},{1},{2})'.format(self._origin, self._destination, self._element)

	# ------------------------- Graph methods -------------------------
	def __init__(self, directed=False):
		"""Create an empty graph (undirected, by default).

		Graph is directed if optional paramter is set to True.
		"""
		self._outgoing = {}
		# only create second map for directed graph; use alias for undirected
		self._incoming = {} if directed else self._outgoing

	def _validate_vertex(self, v):
		"""Verify that v is a Vertex of this graph."""
		if not isinstance(v, self.Vertex):
			raise TypeError('Vertex expected')
		if v not in self._outgoing:
			raise ValueError('Vertex does not belong to this graph.')

	def is_directed(self):
		"""Return True if this is a directed graph; False if undirected.

		Property is based on the original declaration of the graph, not its contents.
		"""
		return self._incoming is not self._outgoing  # directed if maps are distinct

	def vertex_count(self):
		"""Return the number of vertices in the graph."""
		return len(self._outgoing)

	def vertices(self):
		"""Return an iteration of all vertices of the graph."""
		return self._outgoing.keys()

	def edge_count(self):
		"""Return the number of edges in the graph."""
		total = sum(len(self._outgoing[v]) for v in self._outgoing)
		# for undirected graphs, make sure not to double-count edges
		return total if self.is_directed() else total // 2

	def edges(self):
		"""Return a set of all edges of the graph."""
		result = set()  # avoid double-reporting edges of undirected graph
		for secondary_map in self._outgoing.values():
			result.update(secondary_map.values())  # add edges to resulting set
		return result

	def get_edge(self, u, v):
		"""Return the edge from u to v, or None if not adjacent."""
		self._validate_vertex(u)
		self._validate_vertex(v)
		return self._outgoing[u].get(v)  # returns None if v not adjacent

	def degree(self, v, outgoing=True):
		"""Return number of (outgoing) edges incident to vertex v in the graph.

		If graph is directed, optional parameter used to count incoming edges.
		"""
		self._validate_vertex(v)
		adj = self._outgoing if outgoing else self._incoming
		return len(adj[v])

	def incident_edges(self, v, outgoing=True):
		"""Return all (outgoing) edges incident to vertex v in the graph.

		If graph is directed, optional parameter used to request incoming edges.
		"""
		self._validate_vertex(v)
		adj = self._outgoing if outgoing else self._incoming
		for edge in adj[v].values():
			yield edge

	def insert_vertex(self, x=None):
		"""Insert and return a new Vertex with element x."""
		v = self.Vertex(x)
		self._outgoing[v] = {}
		if self.is_directed():
			self._incoming[v] = {}  # need distinct map for incoming edges
		return v

	def insert_edge(self, u, v, x=None):
		"""Insert and return a new Edge from u to v with auxiliary element x.

		Raise a ValueError if u and v are not vertices of the graph.
		Raise a ValueError if u and v are already adjacent.
		"""
		if self.get_edge(u, v) is not None:  # includes error checking
			raise ValueError('u and v are already adjacent')
		e = self.Edge(u, v, x)
		self._outgoing[u][v] = e
		self._incoming[v][u] = e
